Definition:Splitting Polynomial

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Definition

Let $K$ be a field.

Let $P \in K \sqbrk X$ be a polynomial.


Definition 1

$P$ splits (completely) in $K$ if and only if it is a product of polynomials of degree $1$.


Definition 2

$P$ splits (completely) in $K$ if and only if every irreducible factor of $P$ has degree $1$.


Also see

  • Results about splitting polynomials can be found here.